0.999… = 1

Does the title of this post make any sense to you? I just read it in Wikipedia, and now my mind is a little blown.

I’ve never pretended to be any good at math of any kind. I might have gotten more out of it had I ever done any homework in high school, but even if I had paid attention back then I would probably still get a headache trying to work out how much to leave for tips at restaurants. That being said, I do pride myself on a certain level of common sense. And few things satisfy my desire for common sense like an easy-to-follow algebraic formula. Which leads me to the topic at hand.

0.999… is intended to signify a number in which the nines extend an infinite amount of decimal places. Common sense tells me that no matter how many decimal places it extends, however, the number 0.999… is less than 1. That’s the whole point of decimal places, right? They’re another way to represent fractions, like this one:

1/3 = 0.333…

This makes sense. My calculator says so. But then check this shit out:

1/3 = 0.333…1/3 x 3 = 10.333… x 3 = 0.999…0.999… = 1

Who with the what now? That’s half my mind blown right there. But then Wikipedia throws this bomb at me, and I am totally gobsmacked:

c = 0.999…10c = 9.999…10c – c = 9.999… – 0.999…9c = 9c = 1

It makes sense to me if I look at it, but please don’t ask me to explain it. Part of me thinks it’s cool. But it’s a small part. The larger part believes that math is the language with which we will come to understand the universe, and something like this makes me think we may have screwed up some basic part of the grammar, and now we’re translating it all wrong. Should I panic about this? Should I lose faith in my High Priests, the scientists, who hold the keys to the vast and arcane knowledge of the universe? Or is this just some annoying thing that high school AP math teachers whip out because they think it’s funny to make fourteen-year-olds’ heads explode?

Also, on the Wikipedia page it looked all cool ’cause the “=” signs all lined up in the little boxes. Someday I gotta figure out how to do that, but it’s almost one o’clock in the morning. I gotta be up for work in like five hours. This is gonna keep me up all night.

I remember someone pointing out that .33..x3 would never really equal one, and my teacher explained that:

The universe is based on symetry. All things are either made of odds or evens, and can be broken down into either single elements or elements connected to each other. “Thirds” do not truly exist in nature, and therefore trying to create them in math is a conceit.